Sounds like Settlers of Catan would be just about perfect. It has one of those "easy to learn, difficult to master" learning curves, and everyone I've introduced to it has had fun their first time out. It requires skill but there's enough luck involved that you're never really out of it, and if you get bored with the main ruleset you can tack on the Cities and Knights expansion, which really deepens the game a lot (there are others, but that's the best IMO).

There's tons of other fun stuff like Puerto Rico, old-school Axis and Allies, etc., but they're for after you get your feet wet.

ClockworkHouse wrote:

A giant Cthulu alien just threw the top of Big Ben at Abraham Lincoln's airship.

I'm hardly a board game pro, but I'd recommend Carcassonne: very easy rules that allow for very strategic gameplay, simple setup and cleanup, and it scales pretty well from 2-4 players. Some of the scoring rules may make you tear your hair out (e.g. Those Godd*mn Farms), but those all come at the end and aren't as much of an issue, once you get the hang of them.

I've had the best luck introducing friends and family to board gaming outside of Monopoly using the Settlers of Catan, Carcassonne, Ticket to Ride, Blokus, and Tikal.

Ticket to Ride and Blokus in particular are are great ones to introduce to a group of people because the rules and objectives are extremely easy to convey, yet there's plenty of fun and strategy to be had despite the simple foundation.

If you are a fan of Battlestar Galactica you can't go wrong with the BSG board game. It is a fantastic game that combines co-op and traitor gameplay, and it stays very true to the series themes. I would also second the Settlers of Catan and Ticket to Ride recommendations. Finally, you should definitely browse Board Game Geek for suggestions. BGG, has a very comprehensive list of boardgames with tags, community ratings, and discussion boards.

It is definitely a long game with a big rulebook, but my friends and I who aren't huge board game nerds still had a blast with it. I keep getting asked when we're going to get together another session of it.

Ticket to Ride is a fantastic starting point. It is bright and colorful so it looks nice set up on the table and it is also extremely easy to learn. There are several versions; I'd go with the standard (has a map of the USA) but any version will do.

For a second starter game, I'd take a look at either Bohnanza or For Sale. Both are really simple card games that are easy to teach and quite a bit of fun to play. The theme and art on Bohnanza is really bizarre (you are bean farmers trading beans) so that may be a help or hindrance in getting people to try it out. For Sale is all about buying and selling real estate, something everyone can associate with easily and the artwork is great. I think out of everything in my collection For Sale may be the best bang for the buck.

Really anything in this thread is good, though. I would also avoid Battlestar Galactica if you are just starting off. It is a great game - I love it - but it's not a great starting point.

As someone who was in a similar position, Settlers is a great place to start. I've never really gone further than that due to a lack of interest with people I know but I had a lot of fun with it and found it easy enough to get into but with lots of depth once you do.

A lot of great suggestions here. I'll just throw in one more that's a favorite of mine and has been liked by every non-boardgamer I've played it with: RoboRally.

There is a lot of luck in the game play, but there's nothing like trying to guide your increasingly broken robot around a maze of lasers, pits, conveyer belts, and crushers while everyone else is doing the same and trying to kill you.

Personally, I am more into heavily-themed games, and typically I dislike games with a theme I dislike. For instance, farming and realistic trading games...ugh. These bore me. While the mechanics are sound, I simply have no interest in simulating a mundane real life activity within a game.

I want adventure, and big ideas!

Horror themed: Fury of Dracula - this game is awesome. A little on the complex side for beginners, but I really dig this one.

Fantasy Themed: Talisman - as simple as can be, but also really fun. Roll the dice, move around the board, fight monsters and get stuff. It's like Diablo, but without the mouse clicking.

I've had the most success getting casual/non-gamers (my girlfriend, friends of girlfriend, girlfriend of friend, etc...) playing Ticket to Ride, San Juan, and Carcassonne.
They can each be played with 2-5 people, are best with 4 (IMO), and I enjoy Carcassonne the least, although it's still fun to break out every now and then.

I ordered Pandemic last week (birthday present for myself) but it hasn't arrived yet; I'm looking forward to trying it out.

Boardgamegeek is the place to go for boardgame recommendations. Spend a while browsing around there, you will find a LOT of suggestions. If you live in a reasonably populated area, you should have no problem hooking up with other boardgamers through the site. I hope you have more self-restraint than I did...